The distribution of violent event and interevent times in conflicts

arXiv:2501.00027 · physics.soc-ph, physics.data-an · Submitted 2024-12-20 · Read on arXiv

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Introduction to the show: ident: Physics. The day in general physics: instruments, methods and results across the field.

Kai: We're looking at the paper: "The distribution of violent event and interevent times in conflicts".

Mira: Here's the gist of the paper. Enduring violent conflicts are interrupted by lulls without violence Studies of interevent times found power law distributions based on coarse-grained data with a resolution of one day However, when violent conflicts are represented as multiplicative processes and fine-grained data is used, the log normal does not fit better than the power law Therefore, common wisdom is not refuted.

Kai: Conflict Dynamics and Interevent Times Violence occurs between entities ranging from individuals to empires

4: Interruptions occur because opponents move out of the way, individuals stumble, obstacles stand in the way, or other problems occur.

Mira: In most studies, the interevent times turned out to be power law distributed

1, 6, 8: , based on data with a resolution one day.

Kai: However, if the resolution is much finer, a theorem predicts that the distribution of interevent times is lognormal

9: .

Paper summary: Kai: So looking at the "The distribution of violent event and interevent times in conflicts" paper, we see that the common wisdom about power laws is not entirely refuted when you look at finer data <ref:2501.00027#pg3>.

Mira: The authors show that while coarse-grained data points toward power laws, using multiplicative processes with very fine resolution leads to a lognormal fit being better than the power law <ref:2501.00027#pg3>.

Lev: What this means for us is that the underlying mechanism driving these short bursts might be inherently multiplicative, pushing the statistics toward lognormal behavior when you look at event timing <ref:2501.00027#pg2>.

Kai: It suggests that we need to think about how energy and duration scale in violent events, because those physical properties lead to the observed lognormal distribution <ref:2501.00027#pg1>.

Mira: And the authors are careful to note that their data collection had limitations, specifically that single punches were coded as lasting one second because precise measurement was not feasible <ref:2501.00027#pg6>.

Lev: That limitation is key; it tells us the difficulty in getting perfectly clean time measurements for these very short actions, which impacts how we model them on real hardware <ref:2501.00027#pg6>.

Kai: So, the paper confirms that common wisdom isn't totally refuted, but it shows that the actual distribution might be more power law than what we see in coarse data because of sampling bias <ref:2501.00027#pg1>.

Mira: It’s a nuanced point: the tail of the distribution might be undersampled, which biases against power laws compared to what we measure when we look at short durations <ref:2501.00027#pg1>.

Lev: For future work on error correction, this implies that whatever system we build needs to account for this mixture of statistical behaviors: the coarse-grained power law and the fine-grained lognormal reality <ref:2501.00027#pg3>.

Kai: That's it for today on this paper about "The distribution of violent event and interevent times in conflicts."

Conclusion: Kai: So we’ve been looking at how violent conflicts pause and resume, and now we're here to wrap up this paper called "The distribution of violent event and interevent times in conflicts."

Mira: Basically, they found that what you usually see with coarse data—the power law—doesn't hold up when you look really closely at the timing between those events.

Lev: The core finding is that using fine-grained data, like video of street fights, showed a lognormal distribution fitting the timing much better than a power law.

Kai: So what does that actually mean for how we think about these conflicts? Does it mean the power law idea is just an illusion when you look at the raw data?

Mira: It suggests that the way violence actually happens, in terms of those small pauses between fights, isn't purely random in a way that fits a simple power law model.

Lev: From my side, if we were trying to build an error-correction system for real hardware based on this, we’d have to account for this lognormal behavior instead of just assuming the simpler power law scaling.

Kai: I think it means the underlying physics or energy dynamics involved in these short bursts are more constrained than we first thought, which is interesting from a quantum hardware perspective too.

Mira: Exactly. The authors point out that while coarse data looks like power law, the way they modeled the process as multiplicative—which is how you model sequential events—that leads them to predict lognormal behavior.

Lev: And they admit their data had limitations, specifically that single punches were coded as lasting one second because accurate time measurement wasn't feasible in the video recordings.

Kai: That’s a big caveat. So the paper shows that even with those messy, imperfect measurements, if you use a multiplicative process model, the lognormal fit is much stronger.

Mira: It reinforces that for high-resolution studies of conflict dynamics, we should probably be prioritizing lognormal models over the standard power law assumptions based on what we see in everyday data.

Lev: Because when you try to run that kind of statistical analysis on real systems, you have to contend with those kinds of scaling assumptions and measurement errors upfront.

Kai: It definitely makes me wonder how much "noise" there is in the underlying system compared to the signal we’re trying to extract from these conflict timings.

Department of Sociology, University of Amsterdam

physics.soc-ph, physics.data-an

Submitted: 2024-12-20

Updated: 2026-10-29

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 69/100

The gist: Enduring violent conflicts are interrupted by lulls without violence Studies of interevent times found power law distributions based on coarse-grained data with a resolution of one day However, when

Key concepts

Interevent Times
These are the time intervals between violent events in a conflict. The paper examines how these intervals are distributed, specifically testing if they follow a power law (where large gaps are common) or a lognormal distribution (where short gaps are more frequent).
Power Law Distribution
This is a statistical pattern where the probability of an event occurring decreases according to a power function. In conflict studies, this suggests that very long periods of peace might be statistically more likely than in other distributions.
Lognormal Distribution
This distribution describes data where the logarithm of the variable follows a normal (bell-shaped) curve. The paper found that fine-grained conflict data fits this pattern better than the power law, implying that short lulls are more common than predicted by power laws.

Terminology

Summary

Enduring violent conflicts are interrupted by lulls without violence Studies of interevent times found power law distributions based on coarse-grained data with a resolution of one day However, when violent conflicts are represented as multiplicative processes and fine-grained data is used, the log normal does not fit better than the power law Therefore, common wisdom is not refuted.

Conflict Dynamics and Interevent Times

Violence occurs between entities ranging from individuals to empires [4] Interruptions occur because opponents move out of the way, individuals stumble, obstacles stand in the way, or other problems occur. In most studies, the interevent times turned out to be power law distributed [1, 6, 8], based on data with a resolution one day. However, if the resolution is much finer, a theorem predicts that the distribution of interevent times is lognormal [9].

Theoretical Framework

The theory assumes that preparatory actions take a certain amount of time, τ, and in the longer run or over many fights, a distribution of τ settles down. The next interevent time, τ2, can be shorter or longer than τ1, expressed by v1, such that τ2 = v1τ1. After a sequence of t + 1 violent events, the next interevent time can be written as τt+1 = vtvt−1... v1τ1, or log(τt+1) = log(τ1) + Pk=t k=1 vk. The sequence of interevent times is represented as a multiplicative process [3, 5], which to the best of my knowledge is novel for conflict data. Sornette and Cont have proved that in a multiplicative process, τ approaches a lognormal distribution, not a power law.

Empirical Findings from Fine-Grained Data

The study used video recorded street fights between small groups of young men as data. Over 59 fights there are 287 interevent times, ranging from 0.002 to 95 seconds. For the cumulative distribution of interevent times (Fig. 1A), Vuong’s test pointed out that both distributions fit the data approximately equally well (twosided p = 0.403). There are 375 event times, ranging from 0.342 to 36 seconds. For this data, a lognormal fits much better than a power law (one-sided p = 0.00077), in line with my second conjecture.

Discussion and Conclusion

In the scientific community, there is a broad consensus that interevent times are power law distributed [1, 6, 8], based on coarse-grained data. The actual distribution might be more power law than meets the eye, because bystanders lack motivation to keep filming long lulls. Violent events, by contrast, drain energy and last shorter; they were clearly lognormally distributed. The tail of the distribution is probably undersampled, which biases against power laws. Violent events are lognormally distributed because they take much energy and their durations are shorter.

Data and Code

The code and data are at https://osf.io/bpsa6/ The original coded video data is at https://osf.io/f25nq/.

References

[1] Juan Camilo Bohorquez, Sean Gourley, Alexander R. Dixon, Michael Spagat, and Neil F. Johnson Common ecology quantifies human insurgency. Nature, 462:911–914, 2009.

[2] Jeroen Bruggeman, Don Weenink, and Bram Mak Intergroup violence in bursts, 2026. Frontiers in Physics, forthcoming.

[3] R. Gibrat Une loi des r´epartitions ´economiques: l’effet proportionnel. Bulletin de la Statistique G´en´erale de la France, pages 469–514, 1930.

[4] Michael Mann On Wars. Yale University Press, New Haven, 2023.

[5] Michael Mitzenmacher A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1:226–251, 2004.

[6] Hiroshi Okamoto, Iku Yoshimoto, Sota Kato, Budrul Ahsan, and Shuji Shinohara Testing the power-law hypothesis of the interconflict interval. Scientific Reports, 13:22686, 2023.

[7] Susan Olzak Analysis of events in the study of collective action. Annual Review of Sociology, 15:119–141, 1989.

[8] S. Picoli, M. del Castillo-Mussot, H Valentin Ribeiro, E.K. Lenzi, and R.S. Mendes Universal bursty behaviour in human violent conflicts. Scientific Reports, 4:4773, 2014.

[9] Didier Sornette and Rama Cont Convergent multiplicative processes repelled from zero: Power laws and truncated power laws. Journal de Physique I, 7:431–444, 1997.

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The distribution of violent event and interevent times in conflicts Jeroen Bruggeman∗ Department of Sociology, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, the Netherlands. Email: j.p.bruggeman@uva.nl

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is much finer than earlier studies My data is video recorded street fights between small groups of young men.

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The interevent times are random even though the selected videos are not.

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The jump is an artifact of the coding: single punches and kicks were all coded as if they lasted one second, because precise time measurement was not feasible.

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For the cumulative distribution of interevent times (Fig. 1A), I used maximum likelihood estimation of R’s poweRlaw package to fit a lognormal (continuous line) and a power law (dashed line).

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The jump in Fig. 1B is an artifact of the coding: single punches and kicks were all coded as if they lasted one second, because in many cases, accurate time measurement of these behaviors was not feasible.

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For this data, a lognormal fits much better than a power law (one-sided p = 0.00077), in line with my second conjecture.

Improvements for AI systems

  1. Improve event prediction in dynamic conflict environments by modeling interevent times as a lognormal distribution rather than a power law. This allows AI systems to better anticipate lulls without violence based on fine-grained temporal data, as the paper suggests when violent conflicts are represented as multiplicative processes and fine-grained data is used, the log normal does not fit better than the power law.

  2. Enhance short-term behavioral modeling in surveillance systems by using the lognormal distribution for violent event durations. Since Violent events, by contrast, take much energy and their durations are shorter, hence they are lognormally distributed, AI can more accurately estimate the expected length of an immediate physical altercation based on recorded data.

  3. Refine anomaly detection in real-time video streams by distinguishing between interevent times and violent event times using resolution-dependent analysis. This helps systems filter out noise and distinguish interevent times from actual violent events, which is crucial for reliable threat assessment when processing high-resolution, fine-grained video data.

Abstract

Ongoing violent conflicts at all scales are interrupted by lulls without violence. Studies of interevent times found power-law distributions, based on coarse-grained data with a resolution of days or longer. Fine-grained data with a resolution of seconds or shorter is rare. Here, interevent times in violent conflicts are represented as multiplicative processes, and video-recorded street fights are used as fine grained data. For multiplicative processes, a mathematical theorem predicts that coarse grained data are power-law distributed, but fine grained data are lognormal. To the street violence data, however, the lognormal does not fit better than the power law (and vice versa), although the lognormal covers more data. Violent events, by contrast, take much energy and their durations are shorter, hence their distribution is better approximated by an exponential.

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